Exercise
$\pi\int_0^{\pi}\left(\sin\left(x^2\right)\right)dx$
Step-by-step Solution
Learn how to solve integrals of rational functions problems step by step online. Find the integral piint(sin(x^2))dx&0&pi. Rewrite the function \sin\left(x^2\right) as it's representation in Maclaurin series expansion. Simplify \left(x^2\right)^{\left(2n+1\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2n+1. Solve the product 2\left(2n+1\right). We can rewrite the power series as the following.
Find the integral piint(sin(x^2))dx&0&pi
Final answer to the exercise
$\pi \sum_{0}^{\pi }_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(4n+3\right)}}{\left(4n+3\right)\left(2n+1\right)!}+C_0$